Geometric sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Geometric sequences.

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ID	Problem	Count
1051	Find $ a_10 $ of a geometric progression if $ a_1 = 30000 ~~ \text{and} ~~ r = 1.1 $.	5
1052	Find $ a_30 $ of a geometric progression if $ a_1 = 1000000 ~~ \text{and} ~~ r = 1.1 $.	5
1053	Find $ a_20 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = 1.1 $.	5
1054	Find $ a_20 $ of a geometric progression if $ a_1 = 45000 ~~ \text{and} ~~ r = 1.1 $.	5
1055	Find $ a_25 $ of a geometric progression if $ a_1 = 35000 ~~ \text{and} ~~ r = 1.1 $.	5
1056	Find $ a_20 $ of a geometric progression if $ a_1 = 35000 ~~ \text{and} ~~ r = 1.1 $.	5
1057	Find $ a_21 $ of a geometric progression if $ a_1 = 35000 ~~ \text{and} ~~ r = 1.1 $.	5
1058	Find $ a_22 $ of a geometric progression if $ a_1 = 35000 ~~ \text{and} ~~ r = 1.1 $.	5
1059	Find $ a_23 $ of a geometric progression if $ a_1 = 35000 ~~ \text{and} ~~ r = 1.1 $.	5
1060	Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 3 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1061	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.	5
1062	Find $ a_5 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = -5 $.	5
1063	Find $ a_5 $ of a geometric progression if $ a_1 = 1000 ~~ \text{and} ~~ r = -3 $.	5
1064	Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.	5
1065	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -6 $.	5
1066	Find the sum of the first $ 60 $ terms of a geometric sequence if $ a_1 = 1100 ~~ \text{and} ~~ r = 1.05 $.	5
1067	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.	5
1068	Find $ a_7 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -3 $.	5
1069	Find $ a_5 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	5
1070	Find $ a_9 $ of a geometric progression if $ a_1 = 80 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $.	5
1071	Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = 5 $.	5
1072	Find $ a_11 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 2 $.	5
1073	Find $ a_4 $ of a geometric progression if $ a_1 = 54 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $.	5
1074	Find $ a_10 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 3 $.	5
1075	Find $ a_2 $ of a geometric progression if $ a_1 = 54 ~~ \text{and} ~~ r = -\dfrac{ 2 }{ 3 } $.	5
1076	Find the sum of the first $ 19 $ terms of a geometric sequence if $ a_1 = 5 ~~ \text{and} ~~ r = 2 $.	5
1077	Find $ a_10 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1078	Find $ a_7 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = 2 $.	5
1079	Find $ a_11 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 3 $.	5
1080	Find $ a_9 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = 3 $.	5
1081	Find $ a_14 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 2 $.	5
1082	Find $ a_5 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -5 $.	5
1083	Find $ a_17 $ of a geometric progression if $ a_1 = 645700815 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	5
1084	Find $ a_18 $ of a geometric progression if $ a_1 = 645700815 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $.	5
1085	Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 15000 ~~ \text{and} ~~ r = \frac{ 11 }{ 10 } $.	5
1086	Find $ a_4 $ of a geometric progression if $ a_1 = 15000 ~~ \text{and} ~~ r = \dfrac{ 11 }{ 10 } $.	5
1087	Find the sum of the first $ 100 $ terms of a geometric sequence if $ a_1 = 56 ~~ \text{and} ~~ r = \frac{ 1 }{ 8 } $.	5
1088	Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 56 ~~ \text{and} ~~ r = \frac{ 1 }{ 8 } $.	5
1089	Find $ a_7 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 5 $.	5
1090	Find the sum of the first $ 16 $ terms of a geometric sequence if $ a_1 = 50000 ~~ \text{and} ~~ r = 1.04 $.	5
1091	Find $ a_15 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.	5
1092	Find $ a_10 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.	5
1093	Find $ a_9 $ of a geometric progression if $ a_1 = \dfrac{ 5 }{ 16 } ~~ \text{and} ~~ r = 2 $.	5
1094	$$ a_1 = 729 ~,~ r = \frac{ 1 }{ 3 } ~,~ a_n = \frac{ 1 }{ 9 } ~,~ n = ? $$	5
1095	Find $ a_3 $ of a geometric progression if $ a_1 = 50 ~~ \text{and} ~~ r = -\dfrac{ 5 }{ 2 } $.	5
1096	Find $ a_4 $ of a geometric progression if $ a_1 = -4 ~~ \text{and} ~~ r = -2 $.	5
1097	Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 81 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.	5
1098	Find $ a_5 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = 3 $.	5
1099	Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 4 } ~~ \text{and} ~~ r = 2 $.	5
1100	Find $ a_61 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 0.95 $.	5